Vertex-bipancyclicity of the generalized honeycomb tori
- Shih, Yuan-Kang
- Wu, Yi-Chien
- Kao, Shin-Shin
- Tan, Jimmy J.M.
DOIAbstract
AbstractAssume that m,n and s are integers with m≥2,n≥4,0≤s<n and s is of the same parity of m. The generalized honeycomb tori GHT(m,n,s) have been recognized as an attractive architecture to existing torus interconnection networks in parallel and distributed applications. A bipartite graph G is bipancyclic if it contains a cycle of every even length from 4 to |V(G)| inclusive. G is vertex-bipancyclic if for any vertex v∈V(G), there exists a cycle of every even length from 4 to |V(G)| that passes v. A bipartite graph G is called k-vertex-bipancyclic if every vertex lies on a cycle of every even length from k to |V(G)|. In this article, we prove that GHT(m,n,s) is 6-bipancyclic, and is bipancyclic for some special cases. Since GHT(m,n,s) is ...
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